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Beliebt Rechnen >

(\partial)/(\partial x)((x+y)*e^{y^2})

Lösung

\frac{\partial}{\partial x} ((x + y) \cdot e^{y^{2}})

Lösung

e^{y^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + y) e^{y^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{y^{2}} \frac{\partial}{\partial x} (x + y)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= e^{y^{2}} (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y))

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (y) = 0

= e^{y^{2}} (1 + 0)

Vereinfache

= e^{y^{2}}

Beliebte Beispiele

derivative 2cos(2x)

d er i v a t i v e 2 cos (2 x)

derivative f(x)=(ln(x^2))/x

d er i v a t i v e f (x) = \frac{ln ( x ^{2} )}{x}

derivative f(x)=e^{-5x}cos(3x)

d er i v a t i v e f (x) = e^{- 5 x} cos (3 x)

derivative of sin(x+sin(2x))

\frac{d}{d x} (sin (x + sin (2 x)))

integral from-1 to 2 of (x+2)-(x^2)

\int_{- 1}^{2} (x + 2) - (x^{2}) d x